Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology

Experimental characterization of a quantum many-body system via higher-order correlations

“…Within the classical-field approximation, correlation functions of the system at temperature T can be calculated using the transfer-matrix formalism developed in [37,38]. The harmonic approximation (S8) for two tunnel-coupled superfluids has been analysed in [35].…”

“…The transfer-matrix formalism [37,38] yields the following expressions for the thermal average and correlation function of operators O(z):…”

“…The observables O(z) = O(r 1 , θ 1 , r 2 , θ 2 )| z can be arbitrary functions of the classical field provided the integrals exist. The eigenvalues κ n and orthonormal eigenfunctions Ψ n = Ψ n (r 1 , θ 1 , r 2 , θ 2 ) are given by the Hamiltonian-like hermitian operatorK that arises in the transfer matrix formalism [37,38]. For our system of two tunnel-coupled superfluids we havê…”

“…The equilibrium distribution of the real classical variables is determined by the ground (lowest-eigenvalue) state of the operatorK [37,38], via…”

A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein‐Gordon equation

“…In the first approach one assumes that the kinks may be treated as weakly interacting elementary excitations. Provided the kink density is low, the canonical partition function can be found by standard methods [28,29,30]. Alternatively, it is possible to calculate the partition function to exploit a transfer operator technique.…”